Voelker on Relativity
Few people know that relativity was first "coined" by Galileo Galilei (1564-1642). He posited that within a cargo hold of a ship, one could not discern by the movements of a butterfly if the ship was in motion or not. Concomitantly, without a point of reference, one could not discern if the ship was moving with respect to the shore or shore was moving in respect to the ship (e.g.: a rock in entrance of river at ebb tide). Later on, this was called classical mechanics (nothing to do with Mozart), but the theory is known as "Galilean Relativity". Another thing that completely disappeared from public mind was the "luminiferous ether", a mystical substance responsible for the propagation of electromagnetic radiation through space (read light). In my school days, up to the days of the first Sputnik, outer space was still called "the ether" or "the ether of space". The space age finally made do with it. Circa 1887 two American physicist, Michelson and Morley (Michelson was born in Germany) after some tinkering around with some mirrors and studying the interferometry of light (which they could not find) wrote a paper "On the Relative Motion of Earth and the Luminiferous Ether" where they stated that the speed of light is constant and independent of the motion of the emitter or receiver. For light received against the Earth́s motion of translation (30Km/s), or perpendicular to it, always had the same speed. Later on, this was found true for light emanating from a star in motion towards Earth, or from far away galaxies moving away at tremendous speed. The speed of light always measured the same (300.000 Km/s). So "they" named it constant C. Lorentz (Hendrik Anton Lorentz 1853-1928) probably with nothing better to do, decided to fiendishly torture the brains of future physics students, by drawing two superimposed graphs of, one event observed by one, a participant of the event, the other, seeing the event in relative motion to himself. Later writing everything in algebraic notation, which goes by the label of Transformation. Then came some clannish guys, with the attitude of "I know more than you do" and inserted some names, like; inertial frame, frame of reference, causality, invariance, covariance, simultaneity, to name a few. Bradley, not Omar the general, but James (1693-1762) the astronomer, accurately measured the speed of light through a phenomena called "stellar aberration" which is akin to not getting your feet wet by positioning your umbrella everysomore in front of you, depending how fast you run through a calm rain. The light entering the telescope, in this case we assume a star perpendicular to the plane of translation of Earth, is going to hit its wall due to the speed of this translation. A phenomenal feat, considering the tools of the day. After all it is not easy to write mathematics with a quill.
But never fear, for here comes Einstein. He went through the Lorenz transformation like it was child́s play. Then announced to the world, that there is no such thing as "ether". That space and time is a thing, not a factor but a continuum and compresses with motion. Not only light, but measuring tools, your watch, your hand, yourself, everything, and is proportional to the speed of that motion. He wrote a paper "Zür Electrodynamik bewegter Körper" which was later dubbed Special Theory of Relativity. This was in 1905. After mulling over the transformation for two years he coyly got the courage to announce to the world, what is very simple, to those who play with the transformation like a puppy plays with a slipper. E=MC². In between, he wrote a series of papers, like "Über den Einfluss der Schwerkraft auf die Ausbreitung des Lichtes" and finally in march of 1916 his "Die Grundlage der allgemeinen Relativitätstheorie" was published in the Annalen der Physik. The General Theory of Relativity. That same year he wrote his desktop book (for physics students), Relativity, which is an approach in "laymen" terms, about the Special and General Theory of Relativity. The first Theory (Galileós), is but a philosophical dissertation about the relativistic aspect of motion and observers. The second (Einsteińs), is a mathematical proof of the spacetime covariance of simultaneity in the frames of uniform motion... What!? Things shrink when they move. The third (Einsteińs), deals with gravity and accelerated motion which are postulated to be the same. The General Theory has its complications for by dealing with acceleration, which is myriad of little bids of uniform motion, in increasing or decreasing order, uses derivatives, functions and other complicated mathematical juggling that are better left for those that think calculus and polinomes is a piece of cake. The Special Theory is definitely not for Rocket Scientists only, but for any twelveyear old that is attentive and curious. It helps if he/she already knows the Pythagorean theorem. Let́s see. Let́s build ourselves an isosceles triangle in front of us. The base is going to be our time line T. On left angle L we put a flashing device. Right angle R we put a flash detector. Angle directly in front of us M, we put a mirror so that when L flashes the beam of light hits the mirror M, is reflected to sensor R and measured by time T. An isosceles triangle is composed of two right angle triangles which in our case is base T splint in two (2t), to angle M which we name side H. So we have here one rectangular triangle with hypotenuse C (light), one side t (time line) and one side H (for whatever you want.) We can measure C by the Pythagorean equation C²=t²+H². So far so good. Now lets complicate matters a little, by moving this triangle from our right to our left and look at it like we are standing still and measuring the movement. We flash the light, the triangle moves adding time t́́ to our timeframe t́ (everything in our moving timeframe is going to have ́ (prime) to it). Now our equation is going to be Ć= [(t́+t́́)² + H́²]. But wait a minute. Didńt we say before that the speed of light is absolute, or a constant C? So how come we have two values for it? Let́s see if we can unravel this conundrum. We put one observer A, inside the triangle measuring the hypotenuse C. Wherever C goes, A goes. Outside we put observer B. Wherever Ć goes B measures, for he is still, in relation to Ć. A and B are simultaneously measuring C or Ć which is the same event, therefore C is supposed to = Ć but Ć is increased by factor t́́. This only makes sense if you concur that time and or space compresses linearly with motion. In this case t=t́+t́́, being t́́ a relativistic factor "γ?" (gamma) which happens to have its own formula for arriving at. If this does not make sense to you still, then dońt be surprised, for the Nobel commission never came to grasps with it either, for despite Einsteińs later reputation he never got a Nobel prize for it, despite the luminaries of those days, since 1905 consecutively and repeatedly nominated him. In 1922 the Nobel commission saved its red face by giving him the prize for his work in the field of photoelectric phenomena.
If you are still bedazzle by the covariance of the spacetime continuum, let me explain it to you in a more succinct and convincing manner:
E = M C 2 (two)
He pondered, then said it to you.
How did he arrive at that?
Did he use nothing but Math?
Yes he said, there and then,
I used my brain and my pen,
And it was as easy as counting to ten.
Let́s call Energy E
Light we name C
By equating them nicely
We arrive at Matter M, yoúll see.
Math let us shift letters around,
If we have two,
The third can easily be found.
Newton found Mass
When it fell on the grass.
Fizeau found Light,
He was very bright.
Energy was up to me,
And I found it with glee.
They are related these three.
Follow me, and yoúll agree.
Keep in mind,
That math is blind,
Yet with it yoúll find,
What́s in the bind.
For math is a device
That works very nice
The impossible to explain
So it becomes very plain
Then, comes the Lorentz transformation
Which is a big complication
Of causality dissertation
Event graph enumeration
Space time covariation
Tons of mathematical computation
That may give your brain, some constipation
Yet, in the Pythagorean triangle,
The hypotenuse to disentangle,
Which is not a big fandangle
The root, of the squares, of the sides,
The hypotenuse, has to equalize
That is why the transformations
Has roots, inversions, binomial manipulations,
Divisions, squares and lots of multiplications
Which mathematicians call, elegant simplifications
You have to put everything into a frame
In order for the graphics to tame
If voyeur and voyager are not the same
Algebraic notations, is then the game
If all events you carefully plot
Time and Light you throw into the pot
If the Xs, Ys and Zs you haveńt forgot
There is the chance you got the lot
But this does not end here
To the E=MC2 we have to adhere
So let́s go back to the Lorentz transformation
This time using energy manipulation
Which is part of momentum conservation
And fits neatly in the scheme of integration
If you bombard a particle for computation
There is going to be a duality of observation
Inertial observer sees a linear separation
The other a neat triangulation
So, overcoming your braińs constipation
And doing assiduous calculation
Using Pythagorás squares equalization
You arrive at the exclamation
That light remains as self multiplication
For mass and energy did a self annihilation
In the frame of inertial covariation
Through the laws of momentum conservation.
Therefore we arrive with class
That light if squared
Times simple mass
To energy it can be compared
So, dońt despair, despite your plight,
If two observers taking sight
And about spacetime they fight,
If the hypotenuse they make as light,
By the relativistic factor they abide,
It will illuminate and make things bright,
Then everything will be all right
They should come to the allusion
That spacetime is but a fusion
A directional of motion an extrusion,
And therefore shrink... as a conclusion.
© By Percy Voelker